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RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods
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Hu, L., & Bentler, P. M. (1999) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519909540118 · Cited by 108,788
Alternative Ways of Assessing Model Fit
Browne, M. W., & Cudeck, R. (1992) · Sociological Methods & Research · doi:10.1177/0049124192021002005 · Cited by 27,200
Comparative fit indexes in structural models.
Bentler, P. M. (1990) · Psychological Bulletin · doi:10.1037/0033-2909.107.2.238 · Cited by 25,266
Structural model evaluation and modification: An interval estimation approach
Steiger, J. H. (1990) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2502_4 · Cited by 7,408
A Reliability Coefficient for Maximum Likelihood Factor Analysis
Tucker, L. R., & Lewis, C. (1973) · Psychometrika · doi:10.1007/bf02291170 · Cited by 7,330 · cited 2×
“They are the root mean square error of approximation (RMSEA; Steiger, 1990; Steiger & Lind, 1980), comparative fit index (CFI; Bentler, 1990), and Tucker–Lewis index (TLI; Bentler & Bonett, 1980; Tucker & Lewis, 1973).”
BackgroundMethodMarsh, H. W., Hau, K.-T., & Wen, Z. (2004) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem1103_2 · Cited by 6,691
Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012) · Psychological Methods · doi:10.1037/a0029315 · Cited by 2,816
Maximum Likelihood Estimation of the Polychoric Correlation Coefficient
Olsson, U. (1979) · Psychometrika · doi:10.1007/bf02296207 · Cited by 1,127
Factor Analysis with Ordinal Indicators: A Monte Carlo Study Comparing DWLS and ULS Estimation
Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705510903203573 · Cited by 685
Research works printed but not linked: 39
- Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815–824. · DOI
- Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13, 186–203. · DOI
- De Beer, L. T., Pienaar, J., & Rothmann, S. (2014). Job burnout’s relationship with sleep difficulties in the presence of control variables: A self-report study. South African Journal of Psychology, 44, 454–466. · DOI
- Bentler, P. M. (2008). EQS structural equation modeling software. Encino, CA: Multivariate Software.
- Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588–606. https://doi.org/10.1037/0033-2909.88.3.588 · DOI · Paper page
- Brosseau-Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indexes for nonnormality. Multivariate Behavioral Research, 49, 460–470. · DOI
- Brosseau-Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate Behavioral Research, 47, 904–930. · DOI
- Cudeck, R., & Browne, M. W. (1992). Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 57, 357–369. · DOI
- Currier, J. M., & Holland, J. M. (2014). Involvement in abusive violence among Vietnam veterans: Direct and indirect associations with substance use problems and suicidality. Psychological Trauma: Theory, Research, Practice, and Policy, 6, 73–82. · DOI
- DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling, 21, 425–438. · DOI · Paper page
- Fernandez, S., & Moldogaziev, T. (2013). Employee empowerment, employee attitudes, and performance: Testing a causal model. Public Administration Review, 73, 490–506. · DOI
- Garrido, L. E., Abad, F. J., & Ponsoda, V. (2016). Are fit indexes really fit to estimate the number of factors with categorical variables? Some cautionary findings via Monte Carlo simulation. Psychological Methods, 21, 93–111. · DOI
- Iglesias, K., Burnand, B., & Peytremann-Bridevaux, I. (2014). PACIC Instrument: Disentangling dimensions using published validation models. International Journal for Quality in Health Care, 26, 250–260. · DOI
- Johnson, D. R., & Creech, J. C. (1983). Ordinal measures in multiple indicator models: A simulation study of categorization error. American Sociological Review, 48, 398–407. · DOI · Paper page
- Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8: Structural equation modeling with the SIMPLIS command language. Chicago, IL: Scientific Software International.
- Koziol, N. A. (2010). Evaluating measurement invariance with censored ordinal data: A Monte Carlo comparison of alternative model estimators and scales of measurement. Unpublished master’s thesis, University of Nebraska, Lincoln, NE.
- Lai, K., & Green, S. B. (2016). The problem with having two watches: Assessment of fit when RMSEA and CFI disagree. Multivariate Behavioral Research, 51 220–239. · DOI · Paper page
- Li, C. H. (2014). The performance of MLR, USLMV, and WLSMV estimation in structural regression models with ordinal variables (Doctoral dissertation). Michigan State University, East Lansing, MI.
- MacInnis, M. J., Lanting, S. C., Rupert, J. L., & Koehle, M. S. (2013). Is poor sleep quality at high altitude separate from acute mountain sickness? Factor structure and internal consistency of the Lake Louise Score Questionnaire. High Altitude Medicine and Biology, 14, 334–337. · DOI
- Martínez-Rodríguez, S., Iraurgi, I., Gómez-Marroquin, I., Carrasco, M., Ortiz-Marqués, N., & Stevens, A. B. (2016). Psychometric properties of the Leisure Time Satisfaction Scale in family caregivers. Psicothema, 28, 207–213. · DOI
- Maydeu-Olivares, A., Fairchild, A. J., & Hall, A. G. (2017). Goodness of fit in item factor analysis: Effect of the number of response alternatives. Structural Equation Modeling, 24, 495–505. · DOI
- McIntosh, C. N. (2007). Rethinking fit assessment in structural equation modelling: A commentary and elaboration on Barrett (2007). Personality and Individual Differences, 42, 859–867. · DOI
- Muthén, L. K., & Muthén, B. O. (2015). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén.
- Nguyen, T. Q., Poteat, T., Bandeen-Roche, K., German, D., Nguyen, Y. H., Vu, L. K., … Knowlton, A. R. (2016). The internalized homophobia scale for Vietnamese sexual minority women: Conceptualization, factor structure, reliability, and associations with hypothesized correlates. Archives of Sexual Behavior, 45, 1329–1346. · DOI
- Nye, C. D., & Drasgow, F. (2011). Assessing goodness of fit: Simple rules of thumb simply do not work. Organizational Research Methods, 14, 548–570. · DOI
- Pearson, K. (1904). Mathematical contributions to the theory of evolution XIII: On the theory of contingency and its relation to association and normal correlation (Drapers’ Co. Research Memoirs, Biometric Series, no. 1). Cambridge, UK: Cambridge University Press.
- Pettersen, C., Nunes, K. L., & Cortoni, F. (2016). Does the factor structure of the aggression questionnaire hold for sexual offenders? Criminal Justice and Behavior, 43, 811–829. · DOI
- Sass, D. A., Schmitt, T. A., & Marsh, H. W. (2014). Evaluating model fit with ordered categorical data with a measurement invariance framework: A comparison of estimators. Structural Equation Modeling, 21, 167–180. · DOI · Paper page
- Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Thousand Oaks, CA: Sage.
- Savalei, V. (2014). Understanding robust corrections in structural equation modeling. Structural Equation Modeling, 21, 149–160. · DOI
- Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66, 201–223. · DOI
- Stander, F. W., Mostert, K., & de Beer, L. T. (2014). Organisational and individual strengths use as predictors of engagement and productivity. Journal of Psychology in Africa, 24, 403–409. · DOI
- Tallis, G. M. (1962). The maximum likelihood estimation of correlation from contingency tables. Biometrics, 18, 342–353. · DOI
- Xia, Y., Yung, Y. F., & Zhang, W. (2016). Evaluating the selection of normal-theory weight matrices in the Satorra–Bentler correction of chi-square and standard errors. Structural Equation Modeling, 23, 585–594. · DOI
- Yang, Y., & Xia, Y. (2015). On the number of factors in exploratory factor analysis for ordered categorical data. Behavior Research Methods, 47, 756–772. https://doi.org/10.3758/s13428-014-0499-2 · DOI
- Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17, 392–423. · DOI · Paper page
- Yu, C.-Y. (2002). Evaluating cutoff criteria of model-fit indexes for latent variable models with binary and continuous outcomes (Doctoral dissertation). University of California, Los Angeles, CA.
- Yuan, K. H., & Marshall, L. L. (2004). A new measure of misfit for covariance structure models. Behaviormetrika, 31, 67–90. · DOI
- Zhang, W. (2008). A comparison of four estimators of a population measure of model fit in covariance structure analysis. Structural Equation Modeling, 15, 301–326. · DOI
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Zeldovich, M., Bockhop, F., Covic, A., Cunitz, K., Polinder, S., Haagsma, J. A., von Steinbuechel, N., & on behalf of the CENTER-TBI Participants and Investigators (2022) · Journal of Clinical Medicine · doi:10.3390/jcm11164658 · Cited by 36
Elhai, J. D., Casale, S., & Montag, C. (2025) · Journal of Affective Disorders · doi:10.1016/j.jad.2025.03.062 · Cited by 29
Extracting Latent Subdimensions of Social Communication: A Cross-Measure Factor Analysis
Zheng, S., Kaat, A., Farmer, C., Kanne, S., Georgiades, S., Lord, C., Esler, A., & Bishop, S. L. (2021) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2020.08.444 · Cited by 26
Demsash, A. W., Kalayou, M. H., & Walle, A. D. (2024) · BMC Medical Education · doi:10.1186/s12909-024-05680-z · Cited by 21
“…fit indices (GFI > 0.9), adjusted goodness of fit indices (AGFI > 0.8), normal fit indices (NFI > 0.95), Tucker–Lewis index (TLI > 0.9), comparative fit indices (CFI > 0.95), root mean square of standardized residual (RMSSR 0.08), and (RMR 0.08) model fit indices assessment criteria [86, 106].”
BackgroundInfluentialSoto-Sanfiel, M. T., Angulo-Brunet, A., & Lutz, C. (2024) · doi:10.31235/osf.io/bvyku · Cited by 20
Validation and factor structure of the mindfulness-based self efficacy scale-revised
Cayoun, B., Elphinstone, B., Kasselis, N., Bilsborrow, G., & Skilbeck, C. (2022) · Mindfulness · doi:10.1007/s12671-022-01834-6 · Cited by 17
Confirmation and Validation of the Equanimity Scale-16 (ES-16)
Cheever, J., Cayoun, B. A., Elphinstone, B., & Shires, A. G. (2023) · Mindfulness · doi:10.1007/s12671-022-02029-9 · Cited by 14
Listening to and believing derogatory and threatening voices
Sheaves, B., Johns, L., Loe, B. S., Bold, E., Černis, E., Panel, T. M. H. V. L. E. A., Molodynski, A., & Freeman, D. (2023) · Schizophrenia Bulletin · doi:10.1093/schbul/sbac101 · Cited by 8
Gniewosz, G. (2023) · Journal of Youth and Adolescence · doi:10.1007/s10964-023-01808-4 · Cited by 9
Flores-Kanter, P. E., Moretti, L., García-Batista, Z. E., & Medrano, L. (2025) · PLOS One · doi:10.1371/journal.pone.0326319 · Cited by 2
Jeng, A. (2026) · Learning, Culture and Social Interaction · doi:10.1016/j.lcsi.2026.101006
Bansal, S., Kumar, D., & Garg, N. (2026) · International Journal of Conflict Management · doi:10.1108/ijcma-06-2025-0186
Metadata
- Authors
- Xia, Y., & Yang, Y.
- Venue
- Behavior Research Methods
- Published
- 2018-06-04
- Volume
- 51
- Issue
- 1
- Pages
- 409-428
- ISSN
- 1554-351X (ISSN-L)
- 1554-3528
- OpenAlex
- W2806538597
- Cited by
- 1,596
- References
- 9
- FWCI
- 35.18
- Type
- journal article
- Language
- en
- Open access
- bronze
- Licence
- www.springer.com/tdm (tdm)
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